1. **State the problem:** In a class, $\frac{3}{5}$ of the students are girls and the rest are boys. Among the girls, $\frac{2}{9}$ are absent, and among the boys, $\frac{1}{4}$ are absent. We need to find the fraction of the total number of students who are present. 2. **Identify the fractions:** - Fraction of girls = $\frac{3}{5}$ - Fraction of boys = $1 - \frac{3}{5} = \frac{2}{5}$ - Fraction of absent girls = $\frac{2}{9}$ - Fraction of absent boys = $\frac{1}{4}$ 3. **Calculate the fraction of girls present:** - Girls present = Total girls $-$ Absent girls - Fraction of girls present = $\frac{3}{5} \times \left(1 - \frac{2}{9}\right) = \frac{3}{5} \times \frac{7}{9} = \frac{21}{45} = \frac{7}{15}$ 4. **Calculate the fraction of boys present:** - Boys present = Total boys $-$ Absent boys - Fraction of boys present = $\frac{2}{5} \times \left(1 - \frac{1}{4}\right) = \frac{2}{5} \times \frac{3}{4} = \frac{6}{20} = \frac{3}{10}$ 5. **Calculate the total fraction of students present:** - Total present = Girls present + Boys present - $$\frac{7}{15} + \frac{3}{10} = \frac{14}{30} + \frac{9}{30} = \frac{23}{30}$$ 6. **Final answer:** The fraction of the total number of students who are present is $\boxed{\frac{23}{30}}$.